A014323 Three-fold convolution of Bell numbers with themselves.

1, 3, 9, 28, 93, 333, 1289, 5394, 24366, 118526, 618924, 3456942, 20573391, 129951231, 867877107, 6106194478, 45109290477, 348836705235, 2816093142803, 23673989688810, 206794355179656, 1873232870155036, 17565534522745008, 170237112831874188

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

Formula

G.f.: (1/(1 - x - x^2/(1 - 2*x - 2*x^2/(1 - 3*x - 3*x^2/(1 - 4*x - 4*x^2/(1 - ...))))))^3, a continued fraction. - Ilya Gutkovskiy, Sep 25 2017

From G. C. Greubel, Jan 08 2023: (Start)

a(n) = Sum_{j=0..n} A000110(j)*A014322(n-j).

G.f.: ( Sum_{j>=0} A000110(j)*x^j )^3. (End)

Mathematica

A014322[n_]:= Sum[BellB[j]*BellB[n-j], {j, 0, n}];
A014323[n_]:= Sum[BellB[j]*A014322[n-j], {j, 0, n}];
Table[A014323[n], {n, 0, 40}] (* G. C. Greubel, Jan 08 2023 *)

Prog

(Magma)
A014322:= func< n | (&+[Bell(j)*Bell(n-j): j in [0..n]]) >;
A014323:= func< n | (&+[Bell(j)*A014322(n-j): j in [0..n]]) >;
[A014323(n): n in [0..40]]; // G. C. Greubel, Jan 08 2023
(SageMath)
def A014322(n): return sum(bell_number(j)*bell_number(n-j) for j in range(n+1))
def A014323(n): return sum(bell_number(j)*A014322(n-j) for j in range(n+1))
[A014323(n) for n in range(41)] # G. C. Greubel, Jan 08 2023

Crossrefs

Cf. A000110, A014322, A014325.

Column k=3 of A292870.

Sequence in context: A081914 A361763 A120985 * A000752 A047027 A366859

Adjacent sequences: A014320 A014321 A014322 * A014324 A014325 A014326

Keyword

nonn

Author

N. J. A. Sloane

Status

approved